estimation - smu

A method has been Jevrlopecl and used for estlmatlng the erosion drbr~s S~LC’. U. ancl the contact number. c’~. I’& m‘itcrrdl erosion by abrasive water jets with velocities of up to 370 m s. Based on abrasive bsatrr-jet cutting tests on gray cast iron samples. and on measurements of the particle sizes of the rL nu\rd malerial dsbris. the comact number is calculated as the raliu of the number of removed material particles tc) “1~ numhrr ant’ impacti,:, abr-asike particles. the contact numbers ranging bet\veen c-h = 3 and C;, = 1 I. It is found that the contact number increases linearly with the abrasive particle bclocitp in the medium velocity range. bu+ for very low alld very high abrasive velocities the contact number is less influenced by the abrasive velocity. A model is developed for approximating the contact numbers for various cutting conditions. Estimated high contact number:, suggcs~ that a complex impact erosion process may occur which is assGatcd with the formation of a microcrack network by solid particle impact and the uidening of’thr cracks by a high-speed \vatcr fio~ enterin, 0 the crack. (” 1997 Elsevier Science S.A.

As a new manui‘acturing process, abrasive water-jet machining has been very effective in machining difliculit- to-machine materiak. This machining technique is one of the tnost recently introduced machining methods. Abra- i~e water jetting is used for cutting a wide range of materiais, including ceramics [ 1,2]. and composite materials [3.43. As sho,wn in Ref. [5]. abrasive water jets also have the potential for three-dimensional machining. On the basis ofjet generation, abrasive icaterjetscan generally be categorized as injection jets (AIJ) or suspension jets ( ASJ ). For practical applications, AlJs are more commonly used. For this type ofjet,, the pump pressure ranges between 100 and 400 MPa. An AIJ is formed by accelerating small abrasive particles (garnet. aluminum oxide. silicon carbide) through contact with a high velocity plain water jet. A typical abrasive grain diameter is 400 ilrn. The high pressure water isconverted into a high ve?ocity waterjet as

* Corresponding author. WOMA Apparatebau GmbH. Werthaucr Strasse 77- 79, 47226 Duisbtq, German). Fax: f 49 -7065 304 200.

’ Present address: Samsung Electra-Mechanics Co.. Ltd. Seoul. South Korea.

O924-0136~97;!§17.00 8 1997 Elsevicr Science S.A. All rights reserved

SSDI 0924-0136(95)02243-O

it lions Ihroughan orificeon rhe topofthcublasi\ccutting kad. The abrusiws enter the cutting head through ;L separ:t~ inlet. The mixing bet!vecn abrasiws. nater and air takes place in a mixing chamber. and the acceleration process occurs in an acceleration tube, or abrasive water-jet nozzle. The abrasives leave this nozzle at velocities of several hundred meters per second. A high number of abrasive particles ( 10’;s) leads to a high-fre- quency impingement on the materiai being processed. The intensity and the efficiency of the cutting process depend on several process parameters, such as pump pressure. orifice diameter. traverse rate, standoff distance, abrasive Row rate, abrasive type, and mixingchambergeometry [6].

The velocities of the impacting abrasive particles, I\‘~~. can be calculated using the following procedure. Based on a momentum balance in the mixing nozzle it can be shower that:

“‘II Ii’,, = % - (1) l+S

M where z is a mixing and acceleration etfciency coefhcient. For the estimation of the water-jet velocity. IV,,. Bernoulli’s law can be used, which yields:

66 A. W. Monther et al. /Journal of Mate vktls Processing Technology 65 (1997) 65- 72

2P w,=p - J- PW (2)

here p is an orifice efficiency coefficient. The abrasive particle velocity, lop, can now be calculated using Eq. (3):

(3)

During the material removal process, a part of the abrasive water-jet input energy is consumed by the workpiece and contributes to the machining process. As shown in Refs. [7,8] for brittle materials, only a small amount of the abrasive water-jet input energy is used directly to create the target material wear particles, the rest of the energy being dissipated by different mecha- nisms, such as friction, plastic deformation, and damp- ing [9]. A considerable portion of the input energy is carried by the mixture of abrasives, water, and wear particles after it leaves the workpiece [lO,ll]. The energy dissipated in the workpiece significantly influences the machining efficiency, such as the depth of cut and the material removal rate, as well as the machining quality, such as surface roughness and striation formation. It was shown, for example, in Ref. [12] that the erosion rate in abrasive water-jet cutting increases linearly with the kinetic energy of the abrasive particles. The greater is the available energy to feed the dissipa- tion process, the greater is the possible depth of cut in the specimen. For a given depth of cut these relations may determine the quality of the cut surface. In relation to the surface quality parameters, it has been p:oposed in Ref. [13] that the smooth cuttirig zone in the upper part of the cut, which is typically characterized by surface roughness, may be the result of excessive jet energy. There is an excess of jet energy compared with the energy required for the material removal. which contributes to the generation of a comparatively smooth cutting surface. A very similar approach was proposed recently in Ref. [14] suggesting that the available local kinetic energy of the abrasive particles deter- mines the quality of the abrasive water-jet cutting process, especially the formation of striation marks on the cut surface on the lower part of the cut. In Ref. [14] a physical model for the striation formation process was developed and verified e:.perimentally. Also, a significant relationship between the kinetic energy of the abrasive particle and the transition cut depth between smooth cutting zone and rough cutting zone was found. In other words, if the abrasive’s kinetic energy is below a given level, the striation formation ‘process will be introduced. For local energy levels beyond this value the excessive energy contributes to the smoothing of the surfaces as proposed in Ref. [ 131. In Refs. [15,16] a

mathematical model for the estimation of the local abrasive water-jet energy is introduced.

An alternative approach to treat problems related to the material removal process in materials subjected by abrasive water jets is to conduct quantitative investigations on the material particles removed by the high- speed abrasive particle erosion. As shown in Ref. [7& the removed grain samples contain information that can be used successfully to analyse material-removal processes. The subject of this paper is the application and estimation of the so-called ‘contact number’, C,, which is used successfully to evaiuate erosion processes in the field of dry solid particle erosion [17-191 to the abrasive water-jet cutting process.

The behaviour of the cast iron is assumed to be that of a brittle material. Grey cast iron can generally be considered as a two-phase material containing a hard matrix and graphite as a softer second phase. In the grey cast iron, the graphite flakes which can be considered essentially as sharp cracks, inhibit deformation of the normally ductile ferrite and produce a very brittle behaviour. This assumption is supported by experiences in the solid impact and cavitation erosion and impact wear of cast irons. Okada et al. [20] noticed long erosion cracks occurring in grey cast iron because of the severe notching action of the graphite in grey cast iron samples subjected to cavitation erosion. A brittle behaviour of cast iron combined with features of ductile erosion was found in Refs. [21,22] for multiple impact testing. In the two latter references significant features of extensive carbide fracture, de-cohesion at the grain--matrix interface, matrix fracture, and spa11 formation in a narrow zone just below the impacted surface are reported. Laird et al. [23] suggested a merg- ing of crack fronts which originated in pre-existing fractured carbides and resulted in spalling. Radial cracking and fracture in cast iron were also found during the high-speed impact of projectiles [24]. In contrast, Balan et al. [25] observed a maximum solid particle er, Fion of grey cast iron at low impact angles, indicating a tillctile erosion response. Nevertheless, they observed subsuhmface cracking at impact angles of 90”.

2. Contact number estimation

In erosion processes, the contact number, C,, is defined as the ratio of the number of removed wear particles to the number of impacting abrasive particles [18], as given in Eq. (4):

(4)

The number of particles removed from the target specimen, No, can be estimated by Eq. (5) as the ratio of the mass of the removed material to the mass of a single removed wear particle:

h?

Assuming the shape of the removed \vear particles is a mixture of spheres, cubes, tetrahedrons. and octahe-

drons leads to Eq. (6):

VI, 4v,, ~l,-S--.-~-- 0.5230’ nD3

The number of the impacting abrasive particles, N,,. can be calculated by Eq. (4). based on the applied abrasive how rate, M,,, and the time of exposure, f,.:

where the parameter l characterizes the comminution of the abrasive particles during the mixing and acceleration process which was reported in Refs. [26,273 and leads to an increase in the number of impacting abrasive particles on the erosion site. The time of exposure can be estimated by 1,: = L,;‘r-., where I., is the length of the cut. Assuming the shape of the abrasive particles to be spherical, Eqs. (4)~(7) yield:

Eq. (8) contains some important process parameters. such as the traverse rate, cr, and the abrasive flow rate. ;I,?,,. The unknown parameters in this equation are the average particle diameter of the removed target material, D, the average abrasive grain diameter, (I:,. and the volume of the removed material. P’,,. It is important to note that the values of these latter parameters depend on the traverse rate. I+. the abrasive particle velocity. I’,,, and the abrasive feed rate. k,..

Using methods of grain-size distribution analysis [.?S], the average diameter of a grain collection can be estimated by Eq. (9):

Therefore, the average grain diameters D and dir, can be calculated based on a sieve analysis of the removed material samples as well as on the used abrasive material. In order to estimate the average grain diameters of the abrasive and the target materials, and the volume removal on the material sample. cutting experiments, particle collection and sieve analyses were carried out as described in Section 3.

3. Experimental

Fig. 1 shows the flow chart of the experimental work that was done during the investigation. For cutting the

Fig. I. Flo\b chart of the cxprrimcntal work.

specimens. an abrasiv: vvater-jet system was used which consists of a high-pressure intensifier pump, an AWJ cutting head, an abrasive storage and metering system, a catcher tank. and an .~-_I*-: positioning table controlled by a CNC controller. Using a micrometer screw, it was possible to adjust the abrasive mass flow rate. As an abrasive material, garnet # 36 was used, as shown in

Fig. 2. SEM photograph of the abrasive material used (scale = 100 pm).

68 A. W. Mornber er rd. / Jowttd of‘ Mtteriub Processittg Tedtrrolog~ 65 (1997) 65- 72

Table I Cutting conditions and process parameters

Parameter Unit Range

Traverse rate Standoff distance pump pressure Abrasive flow rate Abrasive size Abrasive particle diameter Abrasive material Impact angle Orifice diameter Focus diameter Focus length

mm/s mm MPa g/s mesh

Ctm

0

mm mm mm

4.2 9.0 138-345 4.3 #36 485 Garnet 90 0.33 I .02 76.2

3 it can be concluded that the removal efficiency tends to decrease at comparatively high pressures (in this case p > 300 MPa). This observation is in agreement with trends measured in abrasive water-jet cutting experiments at very high pressures by other researchers [29]. Probably, the cutting process becomes ineffective beyond this pressure range because of a decreased mixing and acceleration efficiency. Based on impact-force mea- surement on plain and abrasive water jets, it was shown in Refs. [11,30] that the efficiency of the energy trans- formation in water-jet orifices and in abrasive water-jet mixing nozzles starts to drop beyond a particular pump pressure: this may generate the drop in the progress of the depth of cut function at comparatively high pump pressures.

Fig. 2. Grey cast iron samples were used as the investi- gated material. The cutting parameters and cutting conditions are listed in Table 1. For catching and collecting the suspension of used abrasives, process water and removed wear particles, a special collection unit was developed which consists primarily of a closed Plexiglas chamber. After cutting, the suspension was removed from the chamber and dried at room tempera- ture. After drying, the cast iron particles and the abrasive grains were separated using a magnet. This process was controlled by periodic inspections using scanning electron microscopy (SEM) and energy dispersive spec- troscopy (EDS) measurements. In order to estimate the grain distributions of the collected wear particle samples, sieve analyses were carried out. The particle move- ment during sieving was performed by a commercial sieve shaker. To estimate the efficiency parameters r and cc in Eqs. (1) and (2) impact-force measurements were performed on plain water jets and abrasive water jets, as described in Ref. [l 11.

4.2. Ar.eruge wcur purtide &meter

A SEM image of a mixture of removed cast iron particles and broken abrasive particles is shown in Fig. 4. Significant differences can be noticed in the surface structures of both materials. The broken abrr+e grains, marked as ‘A’, exhibit large smooth fract areas, indicating unrestrained crack growth. Consider- ing the different magnifications in Figs. 2 and 4, the size reduction during the mixing and cutting process is well documented. The basic mechanism of this size reduction is obviously impact comminution due to impact contact between the abrasive particles and the focus wall or the material sample surface 1261. The cast iron wear particles marked as ‘B’ in Fig. 4 also generally show features of brittle fracture. But in contrast to the abrasive material, the size of the fracture areas are much smaller, which indicates a mixed material removal mode.

4. Results 250

4.1. Materid volunre removal

Fig. 3 shows the relationship between the applied pump pressure, p, and removed cast iron volume, VI,. It can be seen from Fig. 3 that the removed material volume increases linearly with rising pressure, following the relationship:

vo= c, (P-PC) (10)

The intersection between the function and the pressure axis can be identified as a critical threshold pressure, pC. Beyond this pressure range (in this case PC < 60 MPa) no material removal is possible. This threshold value depends strongly on the traverse rate, VT, but it can be applied as a material constant if it is estimated under identical process conditions. From Fig.

0

Fig. 3. Relationship between the applied pump pressure and the material volume removed.

~~~~~~IIIIIIIIIIIIIII~IIIIIIIiI~IIiIII J ,/ I 8 I I I I

Cl 50 100 150 200 250 300 350 400

applied pump pressure in MPa

Fig. 4. SEM photograph of a removed material grain sample ~sc&: 100 pm. applied pressure: 276 MPa). (a) broken abraske grain+. and (b) removed cast iron grains.

Fig. 5 illustrates the influence of the abrasive velocity, IV,,, calculated by Eq. (3) on the average wear particle diameter, D. of the removed cast iron sample. The abrasive particle velocity is used here to compare the estimated wear particle sizes with erosion debris sizes reported from dry solid particle erosion experiments. For the given velocity range. the relationship can be approximated reasonably by a paraboiic function. But from the point of view of the physics of the process it can be assumed that the average wear particle diameter, D. cannot exceed the value of D = 0 if the abrasive velocity does not reach the threshold velocity (~7~ = 130 m;s). which means I\‘,. < u+(.. This assumption indicates that a maximum wear particle diameter ma>

L 8: # .

0 ~~‘,~‘,‘~,‘,~~~~.“‘~~~.‘~~~~r~i~i’~~~~’ 0 50 100 15c 200 250 300 350 400

solid particle velocity in m/s Fig. 5. Relationship between :he solid partic!e velocity and the average wear particle diameter: (1) mild steel. dry solid particle erosion [I@ (2) carbon steel. dry solid particle erosion [ 191: (39 hardened steel. dry solid particle erosion [I 81. and (4) c;Lst iron. abrasive water-jet cutting.

size is comparable with that observed during the dry solid particle erosion of metallic surfaces. as illustrated 0r1 the left section of Fig. 5.

To estimate the direst relationship bctwcen the pump pressure and the contact number it is necessary to quantify the sensitivity of the comminution number, z, defined by Eq. (7). to the applied pump pressure. Therefore, a regression ansiysis of results published in Mcf. [X] was carried out. the regression giving:

% = C’? In p - C, (11) For the pressure range applied in this study the

values for the comminution number are between x = 0.65 and 2 = 0.95. In a previous study [7] it was found that the average grain size of a brittle material, as estintated by Eq. (9) removed by abrasive water jets in the given pressure rang. can be related to the pump pressure by Eq. (I I):

D = cap ’ 5 (12)

Based on Eqs. (IO)--(I?). thr contact number, C,. can be estimated as a function of the applied pump pressure:

(13)

Eq. ( 13) indicates a complex relationship between both parameters. The results of calculations based on Eq. (13) as well as on the experimentally estimated values for & kP. LK and pC are presented in Fig. 6 together with the measured contact numbers, including abrasive particle fragmentation effects. The global relationship between the pump pressure and the contact number C, =fQ), is non-linear. A drop in the function at very high pump pressures can be noticed again. which indicates critical machining conditions existing ;;t a particular pressure level. It seems from Fig. 6 that a ‘sataration’ contact number, C,,,,,, may exist which will be obtained at very high pressure levels. Interest- ingly, in the range of medium pump pressures (p = 150-300 MI%%) the relationship between the pump pressure and the contact number is linear.

The range of the estimated contact numbers lies between CN = 3 and C, = I I. These values are fairly high compared with contact numbers estimated for dry solid particle erosion of metals. To compare abrasive

A. W. Motttber et ul. / Jorrrttni of’ Muterids Proamitg Tecktrolog~ 65 (1997) 65- 7,1 IQ

24

20

1 l6

B f 12

0 8

4

0 0 50 100 150 200 250 300 350 400

pump pressure in MPa

Fig. 6. Relationship between the applied pump pressure and the estimated contact number.

water-jet cutting and dry solid particle erosion, the relationships between the contact numbers and the particle velocities are plotted in Fig. 7. As shown in this figure, contact number values of C, = 0.1-0.25 for soft steel, and values between C, = 0.5- 1.0 for hardened steel eroded by solid particles were found. For the erosion of carbon steel, which showed some features of brittle fracture, contact numbers of C, = 0.2-0.6 were detected 1191. Generally, the contact numbers for solid particle erosion are lower than C, = I, suggesting a

0.1

0 50 100 150 200 250 300 350 400

solid particle velocity in m/s

Fig. 7. Relationship between the solid particle velocity and the contact number for dry erosion and abrasive water-jet erosion: (I) mild steel, dry solid particle erosion [l8]; (2) hardened steel, dry solid particle erosion [ 181: (3) carbon steel, dry solid particle erosion [ 191: (4 and 5) grey cast iron, abrasive water-jet cutting; (4) without abrasive particle comminution, and (5) including abrasive particle comminution.

cumulative solid particle impact that may be necessary to remove an erosive wear particle, For the abrasive water-jet cutting process, it is again assumed that no debris can be removed if the particle velocity is lower than the threshold velocity, Q < MJ~.. It can be noted that under this condition the contact number function crosses the C, = l-line at the particle velocity of rvP = 200 m/s, which is identical to the ‘transition’ velocity noticed in Fig. 5.

5. Discussion

The state-of-the-art analysis of the abrasive water-jet cutting process generally neglects a direct action of the high-speed water on the material surface [31,32], the water jet being considered only as an accelerator for the abrasive particles. This assumption has been validated for a wide range of metallic materials which cannot be cut by plain water jets, but in contrast, pre-cracked materials and materials containing a particular degree of instabilities, such as microcracks and pores, can be cut effectively with plain water jets at commercial pressure ranges [33]. In a classical experiment [34] it was shown that a pre-cracked material cannot be damaged by a plain water jet if it is covered by a very thin metal layer which prevents the high velocity water flow from entering the cracks and pores. if the layer is removed the material fails by internal stresses created in the material by the penetrating water stream. As suggested in Refs. [33,36]. the water enters a crack with high velocities and generates stresses on the crack walls. When the intensity of these stresses exceeds critical local material resistance parameters, such as fracture toughness, the crack will be widened. An intersection of several cracks leads to the formation of a microcrack network and the generation of wear particles. It was shown in Refs. [33,37] for the water-jet cutting of materials that:

(14)

where IV,, is the critical threshold velocity of the water flow. For an undamaged material with l,, =O, the threshold water-jet velocity, IV_, is infinite and the material cannot be cut. However, the water threshold velocity can be reduced significantly when cutting a material containing flaws and cracks. Grey cast iron contains some instabilities because of the graphite flakes in the structure. Nevertheless, undamaged cast iron usually cannot be cut by plain water jets. This situation may change if a particular number of surface cracks is present which can be entered by the high- speed water flow. The formation of surface cracks during the erosion of grey cast iron by solid particles was observed in Ref. [25]. These cracks were still

present during post-erosion SE inspection, ~~~~~c~t~~g that no additional force was present to widen and intersect them. Therefore, several particle impacts arc necessary to remove material debris under this condition. This means that C,; < 1 whit is in fdct the situation in t abrasive water culZing of grcy cast iron with jet locities below t ‘transition’ velocity, IQ < 200 m/s. In this range, t ater velocity is not high enough to widen the cracks generated by abrasive particie impact: thus. Eq. (14) is not satisfi Increasing the jet velocity beyond the ‘tran,sition’ velocity, np < 200 m/s, it can first be assumed that the lengths of the generated crack will increase. Addition- ally, the water flow velocity will increase. A particular combination of both effects will satisfy Eq, (14), which allows the water flow to contribute directly to the material removal process. The water can open isolate cracks and create a crack network. The embedded graphite flakes will reinforce this process, as shown in Ref. [20] for cavitation erosion. This process shows some similarities to a dynamic fragmentation process [7]. Assuming this, the average fragment size will be reduced with increasing loading intensity ]38]: this is well illustrated in Fig. 5. With increasing material removal rate and a decrease in the average wear particle size, the number of removed target particles must increase, yielding larger contact numbers with higher pump pressures, as shown in Fig. 6.

The phenomenologic model supposed above was suggested independently by observations in photo-elastic materials subjected to abrasive water jets. In Ref. ]39], the authors concluded from photo-elastic and SEM studies that an incessant bombardment of abrasive particles created crack nucleation sites with crack growth abetted by the hydro-wedge action of the oncoming water jet.

5. The estimated contact numbers are in the range of Ch = 3 I I. whicfl is higher than the 2on- tact numbers estimated for dry solid particle impact erosion.

6. The contact number increases with the abrasive p;trticic velocity, for low and average particle velocities (pi. = 200-350 m/s) the relationship between abrasive particle velocity and contact number being linear. while for lower an higher particle velocities the progression of the cur

ologic model for a complex mate- anism is supposed combining the rticle impact phenomena and the

erosive action of the QW.

c I 5 constants

6. Co~lcIusions

In this study, investigations on wear particles gcner- ated during the cutting of grey cast iron by abrasive water jets were carried out, the results leading to the following conclusions.

1. An experimental method, based on the sieve analysis of the removed wear particles. can be used to estimate the contact numbers for the abrasive water-jet erosion process in grey cast iron.

2. The material-removal process is characterized by a threshold pump pressure, pc, anti ti threshold abrasive particle velocity, no.

3. The material-removal efficiency is reduced at very x high pump pressures and abrasive particle velocities. %

4. The average diameter of the debris removed by 1’ the abrasive water jet has a maximum value at a PP particular ‘transition’ particle velocity. P\\

contact number sieve diameter for 0.1% ovlerflow average wear particle diameter average abrasive particle diameter sieve diameter for 99.9% overflow grain size distribution parameter water orifice diameter critical stress intensity facto1 critical crack length length of the cut mass of a single wear particle mass of a single abrasive particle mass removal abrasive flow rate water flow rate grain size distribution Farameter number of removed wear particles number of abrasive particles applied pump pressure threshold pump pressure exposure time tsdverse rate volume removal water jet velocity abrasive partic!e threshold velocity water-jet threshold velocity abrasive particle velocity

abrasive focus efficiency parameter comminution number water orifice efficiency number abrasive material density water density

72 A. W. idonrber et al. ~‘Jounrul q/’ Materids Prueessing T~hrolog~~ 65 (1997) 65- 72

Acknowledgements

The authors wish to thank the Alexander-von-Hum- boldt Foundation, Bonn, Germany, and the Center for Robotics and Manufacturing Systems, University of Kentucky, Lexington, for financial support.

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